The routine procedure for designing bridge superstructures relies heavily on the past experience of the designer and is extremely time consuming and costly to try out alternative designs. Typically, a designer is more concerned about satisfying the design requirements laid down by the American Association of State Highway and Transportation Officials (AASHTO) than in coming up with the best possible design from the economic point of view. Thus, application of suitable mathematical programming techniques to determine optimal designs can result in tremendous savings. In this thesis, a procedure based on Generalized Geometric Programming (GGP) is developed to optimally design and select bridge superstructures. The bridge superstructure design problems are formulated as GGP problems incorporating all the design considerations as specified by AASHTO and the Virginia Department of Transportation (VDOT). A primal based algorithm is used in which, the resulting optimization problems are transformed to the solution of a series of Linear Programming problems that are easy to solve. A computer implementation of the algorithm is also developed. The software is extremely versatile and user friendly. It provides several options to help determine the optimal solution under varying design conditions, and is implemented on several representative problems provided by VDOT. Comparison of the resulting optimal with the existing designs promises huge savings in terms of both cost and effort. The methodology that is developed can be used to solve other Engineering Designs Problems as well. / Master of Science